Solve problem using Drawings are recommended, and the use of algebra is encouraged. If you use algebra, make clear what quantity your variable represents. Callie left home at $7:30$ Am to bike eight miles to the school where she taught. Luckily, she could ride on a bike trail where she averaged twelve miles per hour. But at $7:40$ her husband Jeff noticed that she had forgotten to take her graded exam papers, which he knew she wanted to return that day. So he hopped on his bike to catch up with her. If he averaged sixteen miles per hour, did he catch her before she arrived at school? If so, what time did he catch up with her? (Hint: How far could each ride in one minute?)

Use the given property or properties to rewrite each expression. a. (x + 5)x, commutativity of multiplication b. x(4x), associativity of multiplication c. 10n + 10m, distributive property d. y + (3y + 2), associativity of addition e. (4 - 3)x^3, identity for multiplication f. (4/3)n^2 + 0/3 identity for addition.

Write an equation for each of the following using a variable, and then solve the equation: a. Fanny's company has a mortgage debt of $\$ 120$ million and Freddie's company has a mortgage debt of $\$ z$ million. Together, their debt is $\$ 560$ million. What is the mortgage debt of Freddie's company? b. Sidney woke up one morning feeling ill. Her temperature was $104^{\circ}$. She took aspirin and stayed in bed that day. The following morning her temperature was $99.6^{\circ}$. What was the change in her temperature? c. The price of a ticket to Animal World is $\$ 32$ per day. Tanya bought one-day tickets to Animal World and to Air Park for herself and four of her friends for $\$ 300$. What was the one-day price per person at Air Park? d. The price of a ticket to Animal World is $\$ 32$ per day or $\$ 81$ for a three-day pass. If Tanya expected to go for all three days, which type of pass should she buy and why? e. At Amco supermarket the special on mixed nuts from a bin was $\$ 3.68$ per pound. Jenny bought 6 ounces of the nuts. How much did she pay? f. The supermarket in part (e) also had a special on jellybeans. Vinny bought eight ounces of mixed nuts and eight ounces of jellybeans, and his total was $\$ 3.28$. What was the per-ounce cost of the jellybeans?

The collection of ordered pairs, $(2,5),(3,8),(2,9),(5,10)$.

a. What digit is in the thirty eight th place in the calculated form of $\frac{1}{11}$ ? b. What digit is in the $29$ th place in the calculated form of $\frac{3}{7}$ ? c. What digit is in the $43$ rd place in the calculated form of $\frac{1}{9}$ ?

What digit is in the ninty nineth decimal place in the decimal for $\frac{1}{7}$ ? Explain your reasoning.

a. Susan, Rachel, and Steve made six dozen cookies. Over a period of days, they ate them all. Susan ate $25 \%$ more cookies than Rachel ate, and Steve ate two more cookies than Susan ate. How many cookies did each of the three eat? b. Rayann made two dozen deviled eggs for a family gathering, but only she and her two cousins, Nell and Bell, ate any. Together, they ate $\frac{2}{3}$ of the eggs. Rayann ate one-third as many as Nell ate. Bell ate one more than Rayann ate. How many deviled eggs did each eat? c. Anh, Rama, and Amy together ate all of a one-yard-long licorice whip. Anh ate part of it in two minutes at the rate of four inches a minute, Rama ate for $1 \frac{1}{3}$ minutes at a rate of one foot per minute, and Amy finished the whip in three minutes. What was Amy's rate of eating, in inches per minute? (Note: 1 yard $=3$ feet; 1 foot $=12$ inches.) d. Steve and Susan went on a hike on a hot day, with two quarts of water. During the hike, Susan drank a half pint of water more than Steve did. They drank all of the water. How much water did each of them drink? (Note: 1 quart $=2$ pints.)

Complete the following subtractions and tell how they are alike: a. 7/9 - 2/9 b. 2x/7y - 4/7y

In each part, write the property or properties being used. a. replacing 6x + 4x with 10x b. rewriting (7x + 2) + ax as (7x + ax) + 2 (two properties) c. thinking of (15x)(17y) as (15 • 17)(xy) (two properties) d. replacing 3x + ̅ 7x + ̅ 5x with (3 + ̅ 7 + ̅ 5)x e. replacing xy + xz with x(y + z) f. replacing (x + 2)(x + 7) with x(x + 7) + 2(x + 7).

Below mentioned argument, used to justify the result for the row with hundred squares, could be modified to justify the general $3 n+1$ result for a row of $n$ squares, from Activity we saw earlier ? If an argument is not strong, explain why. Ricky: "Everyone I asked said the same thing, $301$ ."

Which of the following are solutions to $x^3-3 x^2=10 x$ ? a. Zero b. Two c. $-2$ d. Four e. Five f. $-4$

Solve problem using Drawings are recommended, and the use of algebra is encouraged. If you use algebra, make clear what quantity your variable represents. A town has been using a recycling plan for three years. The second year of the plan saw an increase in recycled tonnage of $25 \%$ over the first year, and the third year saw an increase of $20 \%$ over the second year. The mayor proudly claims, "During those three years, we have saved $41,250$ tons of trash from being put into our landfill." How many tons were recycled each of the three years? (Hint: For the third year, you will probably want an expression for $120 \%$ of the expression for the second year.)

Use the shortcut method from Activity we saw earlier to find $85^2$ and $19.5^2$.

Complete the following additions and tell how they are alike: a. 5/8 + 3/4 b. {3x/(x+2)(x+3)} + 2/(x+2)